Orbital Ingredients for Cooking X-structures in Edge-on Galaxies

X-structures are often observed in galaxies hosting the so-called B/PS (boxy/peanuts) bulges and are visible from the edge-on view. They are the most notable features of B/PS bulges and appear as four rays protruding from the disk of the host galaxy and distinguishable against the B/PS bulge background. In some works, their origin is thought to be connected with the so-called banana-shaped orbits with a vertical resonance 2:1. A star in such an orbit performs two oscillations in the vertical direction per one revolution in the bar frame. Several recent studies that analyzed ensembles of orbits arising in different N-body models do not confirm the dominance of the resonant 2:1 orbits in X-structures. In our work, we analyze two N-body models and show how the X-structure in our models is gradually assembled from the center to the periphery from orbits with less than 2:1 frequency ratio. The most number of such orbits is enclosed in a "farfalle"-shape (Italian pasta) form and turns out to be non-periodic. We conclude that the X-structure is akin to the envelope curve of regions of high density caused by the crossing or folding of different types of orbits at their highest points, and does not have a "backbone" similar to that of the in-plane bar. Comparing the orbital structure of two different numerical models, we show that the dominance of one or another family of orbits with a certain ratio of the vertical oscillations frequency to the in-plane frequency depends on the parameters of the underlying galaxy and ultimately determines the morphology of the X-structure and the opening angle of its rays.